Finite Group DatabasebetaFinite Group Databasebeta| order | 37980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic3×C211⋊C3 |
| unambiguous semidirect product | C3⋊(C4×C5×C211⋊C3) |
| unambiguous semidirect product | (C5×Dic3×C211)⋊C3 |
| derived | C3×C211 ⋊ C3×C4×C5 |
| Hall | C3×C5×C211⋊C3 ⋊ C4 |
| Hall | C3×C211⋊C3 ⋊ C4×C5 |
| Hall | C5×C211 ⋊ C3×Dic3 |
| Sylow | C211 ⋊ C3×C5×Dic3 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12660 |
2190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37980, 70);